Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

Area of Science:

• Computational Quantum Chemistry
• Quantum Monte Carlo Methods

Background:

• Accurate calculation of electronic structure properties is crucial in chemistry and physics.
• Full configuration interaction quantum Monte Carlo (FCIQMC) is a powerful method for obtaining exact solutions in electronic structure theory.
• Efficient and unbiased sampling of reduced density matrices (RDMs) is essential for accurate property calculations.

Purpose of the Study:

• To develop an unbiased stochastic sampling method for one- and two-body reduced density matrices within FCIQMC.
• To extend the applicability of FCIQMC to properties not necessarily commuting with the Hamiltonian, such as analytic nuclear forces and dipole moments.
• To validate the new sampling technique by comparing results with exact calculations and experimental data.

Main Methods:

• Introduction of a second, independent 'replica' ensemble of walkers in FCIQMC.
• The replica ensemble evolves in imaginary time, enabling unbiased sampling of RDMs.
• Utilizing a density-matrix formulated quasi-variational energy estimator.

Main Results:

• The replica ensemble method achieves unbiased stochastic sampling of RDMs with modest computational overhead.
• Obtained RDMs are of full configuration-interaction quality, enabling accurate property calculations.
• The method successfully computes analytic nuclear forces, molecular dipole moments, and polarizabilities, showing close agreement with exact and experimental results.

Conclusions:

• The replica ensemble technique significantly expands the scope of FCIQMC for calculating a wider range of molecular properties.
• This method provides a realistic pathway to high-quality computational chemistry results for challenging systems.
• The validated sampling technique demonstrates suitability for new areas of quantum chemical investigation.